<!DOCTYPE html>
<html lang="en-US">
<!--********************************************-->
<!--*       Generated from PreTeXt source      *-->
<!--*                                          *-->
<!--*         https://pretextbook.org          *-->
<!--*                                          *-->
<!--********************************************-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>If <span class="process-math">\(\lambda=-k^2&lt;0\text{,}\)</span> then</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y(x)=c_1e^{kx} + c_2e^{-kx},\quad y'(x)=kc_1e^{kx} - kc_2e^{-kx}
\end{equation*}
</div>
<p class="continuation">To determine <span class="process-math">\(c_1\text{,}\)</span> <span class="process-math">\(c_2\text{,}\)</span> use the boundary conditions:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
kc_1-kc_2=0,\quad kc_1e^{kL}-kc_2e^{-kL}=0,\quad\Rightarrow\quad c_1=c_2=0
\end{equation*}
</div>
<p class="continuation">which gives only trivial solution (Discard).</p>
<span class="incontext"><a href="sec7_2.html#p-327" class="internal">in-context</a></span>
</body>
</html>
